y=3x+11 1. Find y if x=3 2. Find y if x= -2 Warm up y=3x+11 1. Find y if x=3 2. Find y if x= -2

Objective You will be able to: Solve systems of equations using substitution, when one variable is already alone.

Solving Systems of Equations You can solve a system of equations using different methods. The idea is to determine which method is easiest for that particular problem. These notes show how to solve the system algebraically using SUBSTITUTION.

Solving a system of equations by Substitution: 5 Stepsubstitution Step 1: Solve an equation for one variable. Pick the easier equation. The goal is to get y= ; x= ; a= ; etc. Step 2: Substitute Put the equation solved in Step 1 into the other equation. Step 3: Solve the equation. Get the variable by itself. Step 4: Plug back in to find the other variable. Substitute the value of the variable into the equation. Step 5: Check your solution. Substitute your ordered pair into BOTH equations.

Example 1: Solve the system using substitution x + y = 5 y = 3 + x Step 1: Solve an equation for one variable. The second equation is already solved for y! Step 2: Substitute x + y = 5 x + (3 + x) = 5 2x + 3 = 5 2x = 2 x = 1 Step 3: Solve the equation.

Example 1 Continued… x + y = 5 y = 3 + x x + y = 5 (1) + y = 5 y = 4 Step 4: Plug back in to find the other variable. (1, 4) (1) + (4) = 5 (4) = 3 + (1) Step 5: Check your solution. The solution is (1, 4). What do you think the answer would be if you graphed the two equations?

Example 2 2x − 3y = −1 y = x − 1 The second equation is Step 1: Solve an equation for one variable. The second equation is already solved for y! Step 2: Substitute 2x - 3y = -1 2x - 3(x-1) = -1 2x - 3x + 3 = -1 -x = -4 x = 4 Step 3: Solve the equation.

Example 2 Continued… 2x − 3y = −1 y = x − 1 y = x − 1 y = (4) - 1 Step 4: Plug back in to find the other variable. (4,3) (8) - (9) = -1 (3) = (4) - 1 Step 5: Check your solution. The solution is (4,3). What do you think the answer would be if you graphed the two equations?

You Try! Which answer checks correctly? 3x – y = 4 x = 4y - 17 (2, 2) (5, 3) (3, 5) (3, -5)

Homework Systems By Substitution Worksheet All problems